A.8 Direct and Inverse Variation

Lesson on Direct and Inverse Variation

Please make sure to write notes as you are reviewing each slide.

Some text here about the topic of discussion

What is 'Variation'?

• Variation is a relationship between 2 or more situations (variables) that have an unchanged constant of variation (k)

• Examples:

• The way grades are related to the hours of study

• The way temperature is related to attendance at a baseball game

• The way hours worked is related to the amount of a paycheck

Direct Variation:

• The graph is a line that passes through (0, 0)

• k is the constant of proportionality and the slope of the line

• As one variable increases or decreases the other does the same

Multiple Choice

Which graph shows a relationship that varies directly?

Multiple Choice

Which graph shows a relationship that varies directly?

Multiple Choice

Which equation represents a relationship with direct variation?

• y = -3x

• y = 0.25x - 1

• y = 4x + 5

Multiple Choice

Which equation DOES NOT represent a relationship with direct variation?

• y = -7x

• y = 4x + 7

• y = 3.5x

Multiple Choice

Which of the following represents direct variation?

• y = kx

• y = k/x

• y = x/k

• y = mx + b

Multiple Choice

Is the given table a direct variation? If so, what is the constant?

• Yes; 1/4

• Yes; 4

• Yes; 2

• No

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3

• Yes; 3

• Yes; 5

• No

Multiple Choice

The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

• $2

• $308

• $1.57

• $265

Multiple Choice

y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

• y = 1344x

• y = 100x

• y = 5.25x

• y = 4/21x

Multiple Choice

Does the equation show an inverse variation? 

$$y=\frac{10}{x}$$  

• yes 

• no

Multiple Choice

What kind of variation does this equation show?

y = 6x

• Inverse Variation

• Direct Variation

• Joint Variation

• No Variations

Multiple Choice

Given the following equation, identify the constant k.

$$y=\frac{54}{x}$$  

• There is none

• y = k

• k = x

• k = 54

Multiple Choice

True or False:

Inverse Variation passes through the origin of a graph and Direct Variation does not.

• True

• False

Multiple Choice

Identify the table:

Direct, Inverse, Or neither?

• Direct

• Inverse

• I don't Know

Multiple Choice

Identify the table:

Direct, Inverse, Neither

• Direct

• Inverse

• Neither

Multiple Choice

Identify the table:

Direct, Inverse, Or neither?

• Direct

• Inverse

• I don't know

Multiple Choice

True or False:

An Inverse Variation is always a curve and a Direct Variation is always a line?

• True

• False

Multiple Choice

What type of variation does this graph represent?

• Direct

• Inverse

• Neither

Multiple Choice

What type of variation does this graph represent?

• Direct

• Inverse

• Neither

Identify an Inverse Variation from a Table

Multiple Choice

Write the equation for the table given.

• $$y=\frac{1}{3}x$$

• $$y=\frac{48}{x}$$

• $$y=3x$$

• $$y=\frac{3}{x}$$

Multiple Choice

What is the constant (k) in this inverse variation?

• 12

• 48

• 24

• Not enough information given

Multiple Choice

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct, 12

• Direct, $$\frac{1}{12}$$

• Inverse, 12

• Inverse, $$\frac{1}{12}$$

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

• Yes, $$\frac{1}{3}$$

• Yes, 5

• Yes, 3

• No

Multiple Choice

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

• 14

• 2

• 10

• -14

Multiple Choice

x and y vary inversely. Given (5, 20), what is the constant k?

• 4

• 25

• 5

• 100

Multiple Choice

The volume V of a gas kept at a constant - temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What type of variation problem is this and which is the formula?

• Direct; $$V=k\cdot p$$

• Inverse; $$V=\frac{k}{p}$$

• Direct; $$p=k\cdot V$$

• Inverse; $$p=\frac{k}{V}$$

Multiple Choice

The amount of money spent at the gas station varies directly with the number of gallons purchased. When 11.5 gallons of gas were purchased the cost was $37.72. Write the equation?

• $$37.72=k⋅11.5$$

• $$37.72=11.5\cdot k​$$

• $$m=3.28⋅g$$

• $$m=\frac{433.78}{g}$$

Multiple Choice

The time to complete a project varies inversely with the number of employees. If 3 people can complete the project in 7 days, how long will it take 5 people?

• t = 4.2 days

• t = 21 days

• t = 5 days

• t = 3 days